Conception ..

If I had sex June 24th and 27th unprotected, using the pull out method.. got my period the 30 which lasted 3 days as it was supposed to. could I have gotten pregnant one of those days? I am pregnant now, and when I count back, it says I conceived July 1st, but that cycle day 2 for me.. I was thinking I got pregnant afterwards, because the dates of sex and my period was too close.. but I just wanted other opinions..